Due to its many applications in several fields of physics, the Schrödinger equation in a position-dependent mass (PDM) background has arisen much interest over the years [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}. Finding exact solutions of such a Schrödinger equation turns out to be very useful for understanding some physical phenomena and testing some approximation methods. Several techniques are available for generating PDM and potential pairs leading to such exact solutions (see, e.g., [13]}, [14]}, [15]} and references quoted therein). Among them, one may quote the point canonical transformation (PCT) applied to an exactly-solvable constant-mass Schrödinger equation [16]}, which has proved very useful to achieve this goal (see, e.g., [17]}, [18]}, [19]}).
